Mr. Jones went to a bank to cash a check. The teller switched the dollars and cents. Mr. Jones was given dollars instead of cents and cents instead of dollars. After buying a five-cents newspaper, Jones discovered that he had exactly twice as much as his original check. What was the amount of the check?
Suppose his check was worth $d and c cents, or 100d+c (d,c < 100).He was given 100c+d, and after the newspaper had (100c+d-5)=2(100d+c)
100c+d-5=200d+2c
98c=199d+5
0=3d+5 (98)
93=3d (98)
We can't divide through mods but we can multiply by 33 (same result anyways)
31=d (98)
As 0
Suppose his check was worth $d and c cents, or 100d+c (d,c < 100).He was given 100c+d, and after the newspaper had (100c+d-5)=2(100d+c)
100c+d-5=200d+2c
98c=199d+5
0=3d+5 (98)
93=3d (98)
We can't divide through mods but we can multiply by 33 (same result anyways)
31=d (98)
As 0 is less than d is less than100, d=31 and it follows that c=63
The check was worth $31.63
Sorry about the double post, for some reason all the text after i typed the 'less than to' sign was cut off. I dunno why that didn't happen with my first one though. Wierd.
you need two independent equations.
The original check was for the amount of 100d + c cents
he got 100c + d cente
100d + c - 5 = 200d + 2 c ... first equation
The second equation: we know c has to be bigger than d. c should either be twice d or c = 2d+1
solve:
1. 100d + c - 5 = 200d + 2c
2. c = 2d+1
Answer: 31 dollars 63 cents